English

Nonlinear Roth type theorems in finite fields

Number Theory 2016-08-22 v1

Abstract

We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of the operators leads to different phenomena, both qualitatively and quantitatively.

Keywords

Cite

@article{arxiv.1608.05448,
  title  = {Nonlinear Roth type theorems in finite fields},
  author = {Jean Bourgain and Mei-Chu Chang},
  journal= {arXiv preprint arXiv:1608.05448},
  year   = {2016}
}
R2 v1 2026-06-22T15:23:51.965Z